Study of near-field coupling in whispering gallery mode resonators

In this paper, an analytical framework is developed to study the performance of a planar-interface near-field coupler into a whispering gallery mode (WGM) resonator. We focus on the efficient coupling of a Gaussian beam under total internal reflection (TIR) at the planar interface of a lens, which is near a spherical resonator. The aim is to optimize the coupling in WGM nonlinear resonators, for high-sensitivity mm-wave signals receivers. Arbitrarily-shaped resonators can be also studied since they are modeled by using the T-matrix method. The inverse problem for obtaining the optimal incident field configuration in order to excite a given WGM inside the resonator can also be solved. This framework can be extended to work with arbitrarily-shaped couplers as well.